Time-dependent density-functional approach for exciton binding energies

Optical processes in insulators and semiconductors, including excitonic effects, can be described using time-dependent density-functional theory (TDDFT) in linear response, provided one uses suitable long-range exchange-correlation (XC) kernels. We derive a conceptually and computationally simple formalism for calculating exciton binding energies with TDDFT which is convenient for testing different XC kernels. The formalism is based on a linearization of the TDDFT semiconductor Bloch equations within a two-band model and gives rise to an eigenvalue equation in momentum space which directly yields exciton binding energies; these can be accurate even if the underlying Kohn-Sham band gap is not. Exciton binding energies are calculated for several direct-gap semiconductors and insulators using exchange-only and model XC kernels.